We can frame no mechanical definition of life! Nor is this the only example offered by experience of a term applied exclusively to mechanisms and yet meaning nothing mechanical. Let me give a homely illustration. There is, I presume every one would admit, no time-piece which is not a machine. And yet we can offer no mechanical definition of a time piece, for the simple reason that the various machines to which this term applies have no mechanical principle in common. A class which may include such divers mechanisms as a sun dial, an hour glass, a water clock, a pendulum clock, a spring watch, a chronograph, has evidently not been given a single name to mark in the members composing it a single mechanical nature. The only thing these members have in common is a certain function or purpose,--that of producing a movement keeping pace with the apparent motion of the sun. Just so with the class of beings we call living. Each of them at each moment of its existence is a complete illustration of mechanical law, yet all of them offer such divers illustrations of this law that they cannot have been put into a single class because of a common mechanical nature. That which they have in common, by virtue of which they have been grouped under one name, is once more a function or a purpose. For we observe that living things, by whatever mechanical devices, accomplish for the most part a common result, that of self-preservation. In these two examples, the one taken from the inanimate, the other comprising the animate world, we see how well it may come about that a certain character belong to a whole, no vestige of which is to be found in its constituent parts. A single atom cannot, if the mechanical ideal is maintained, be regarded as acting purposefully, yet a sufficiently complex group of atoms may well enough display purpose in its behavior and to that purpose owe its right to the name we give it. In such cases the real absurdity we are in danger of committing is not the one that Adrien Sixte scoffs at, but the one he unsuspectingly falls into. Axioms of addition are excellent guides for those whose problem is to add. But not all composition of parts into a whole is so simple as the business of forming a sum. And where we are not adding, the axioms of addition may prove the worst of company.